Most sites that do Shockwave/Flash videos give you a method for embedding their videos onto your own websites. However, the method that PHPBB2 uses requires a little bit of investigation. It should also be noted that some sites won't work at all.

First, click the EMBED portion of the site you're gleaning the video from. Example 1 will be YouTube...

Underneath the video you'll see a box that says SHARE. Click in the box, it display the "short" URL of the video, and just under that will be a button that says EMBED. A box will appear with the embed code DON'T USE IT. Check the box just beneath the code that says USE OLD EMBED CODE. Right click and COPY the code that now appears in the window.

On the message board, open up your new message (or reply). Right click and PASTE the code into the editor.